A polynomial with constant coefficients satisfied by a commuting pair of differential operators is called a Burchnall–Chaundy \((\) BC\()\)  polynomial, since the first result of this sort appeared is the 1923 paper [1]} by Burchnall and Chaundy. In fact, they showed that the converse is also true, namely if two (non-constant) operators satisfy identically a polynomial in two indeterminates \(\lambda \) , \(\mu \)  that belongs to \(\mathbf {C}[\lambda ,\mu ]\) , then they commute.
